In this paper, we investigate channel sensing and power control problems in a cluster-based cognitive radio wireless sensor network (CRWSN). We first propose three channel sensing algorithms to solve the channel sensing problem including availability constraints. Then a joint channel sensing and power control scheme (JCSPCS) is proposed to solve the power control problem including quality of service (QoS) constraints. We prove that all our algorithms are probably approximately correct (PAC) algorithms that can correctly identify a bad channel with high probability. We show that our algorithms are suitable for QoS-constrained applications as they all terminate in a finite time with a finite error rate. The performance of our channel sensing algorithms and the joint channel sensing and power control scheme is shown in the simulation results.